Resonator electrode configuration to avoid capacitive feedthrough for vibrating beam accelerometers

ABSTRACT

This disclosure describes techniques of configuring capacitive comb fingers of an accelerometer resonator into discreet electrodes with drive electrodes and at least two sense electrodes. The routing of electrical signals is configured to produce parasitic feedthrough capacitances that are approximately equal. The sense electrodes may be placed on opposite sides of the moving resonator beams such that the changes in capacitance with respect to displacement (e.g. dC/dx) are approximately equal in magnitude and opposite in sign. The arrangement may result in sense currents that are also opposite in sign and result in feedthrough currents of the same sign. The sense outputs from the resonators may be connected to a differential amplifier, such that the difference in output currents may mitigate the effect of the feedthrough currents and cancel parasitic feedthrough capacitance. Parasitic feedthrough capacitance may cause increased accelerometer noise and reduced bias stability.

This application claims the benefit of U.S. Provisional PatentApplication 62/932,397, filed 7 Nov. 2019, and U.S. Provisional PatentApplication 62/932,298, filed 7 Nov. 2019, the entire contents of eachbeing incorporated herein by reference.

TECHNICAL FIELD

The disclosure relates to vibrating beam accelerometers.

BACKGROUND

Accelerometers function by detecting a displacement of a proof massunder inertial forces. In one example, an accelerometer may detect thedisplacement of a proof mass by the change in frequency of a resonatorconnected between the proof mass and a support base. A resonator, whichmay be designed to change frequency proportional to the load applied tothe resonator by the proof mass under acceleration. The resonator may beelectrically coupled to signal generation circuitry forming anoscillator, which causes the resonator to vibrate, and in some examplesat the resonant frequency of the resonator.

SUMMARY

In general, the disclosure provides techniques to improve the functionof vibrating beam accelerometers (VBA). In one example, the disclosuredescribes techniques to damp the proof mass motion of an accelerometerwhile achieving an underdamped resonator. In an example of an in-planemicro-electromechanical systems (MEMS) VBA, the proof mass may containone or more damping combs that include one or more banks of movable combfingers attached to the proof mass. The movable comb fingers may beinterdigitated with anchored comb fingers that are attached to fixedgeometry. These damping comb fingers may provide air damping for theproof mass when the MEMS die is placed into a pressure cavity of apackage containing a pressure above a vacuum. In some examples, the MEMSdie may be placed into a ceramic package that contains a pressure ofapproximately 1 Torr. The geometry of the damping combs may minimize theair gap and maximize the overlapping area between the movable combfingers and anchored comb fingers. The geometry of resonator of the VBAof this disclosure may be configured to avoid air damping.

In other examples this disclosure describes techniques of configuringcapacitive comb fingers of an accelerometer resonator into discreetelectrodes with a drive electrode and at least two sense electrodes. Thetechniques of this disclosure further describe the routing of electricalsignals on the die and on the analog electronics board designed toproduce parasitic feedthrough capacitances that are approximately equal.The at least two sense electrodes may be placed on opposite sides of themoving resonator beams such that the changes in capacitance with respectto displacement (e.g. dC/dx) are approximately equal in magnitude andopposite in sign. This may result in sense currents that are alsoopposite in sign and result in feedthrough currents will be of the samesign. The sense outputs from the resonators may be connected to adifferential front-end amplifier, such as a transimpedance or chargeamplifier, which processes the difference in output currents. Processingthe difference in output currents may mitigate the effect of thefeedthrough currents and cancel parasitic feedthrough capacitance.Parasitic feedthrough capacitance may cause increased accelerometernoise and reduced bias stability.

In other examples, the disclosure describes a vibrating beamaccelerometer (VBA) device, the device comprising: a resonatorcomprising: a resonator beam; a drive electrode; and a first senseelectrode and a second sense electrode, wherein: the first senseelectrode is located on a first side of the resonator beam, the secondsense electrode is located on a second side of the resonator beamopposite the first side such that a first change in capacitance withrespect to displacement (dC₁/dx) for the first sense electrode isapproximately equal in magnitude to a second change in capacitance withrespect to displacement (dC₂/dx) for the second sense electrode andopposite in sign; and electrical signal routing comprising: a drivesignal path coupled to the drive electrode; a first sense signal pathcoupled to the first sense electrode; and a second sense signal pathcoupled to the second sense electrode. The electrical signal routing isconfigured to produce: a first parasitic capacitance between the drivesignal path and the first sense signal path that generates a firstparasitic feedthrough current; and a second parasitic capacitancebetween the drive signal path and the second sense signal path, thatgenerates a second parasitic feedthrough current, such that the firstparasitic feedthrough current and the second parasitic feedthroughcurrent are approximately equal in magnitude.

In other examples, the disclosure describes A method comprising:receiving, by processing circuitry, one or more electrical signalsindicative of a frequency of a first resonator beam and a frequency of asecond resonator beam from a vibrating beam accelerometer (VBA), whereinthe VBA comprises: a resonator comprising: the first resonator beam; adrive electrode; and a first sense electrode and a second senseelectrode, wherein: the first sense electrode is located on a first sideof the resonator beam, the second sense electrode is located on a secondside of the resonator beam opposite the first side such that a firstchange in capacitance with respect to displacement (dC₁/dx) for thefirst sense electrode is approximately equal in magnitude to a secondchange in capacitance with respect to displacement (dC₂/dx) for thesecond sense electrode and opposite in sign; and electrical signalrouting: comprising: a drive signal path coupled to the drive electrode;a first sense signal path coupled to the first sense electrode; and asecond sense signal path coupled to the second sense electrode, whereinthe electrical signal routing is configured to produce: a firstparasitic capacitance between the drive signal path and the first sensesignal path that generates a first parasitic feedthrough current; and asecond parasitic capacitance between the drive signal path and thesecond sense signal path, that generates a second parasitic feedthroughcurrent, such that the first parasitic feedthrough current and thesecond parasitic feedthrough current are approximately equal inmagnitude, and determining, by the processing circuitry and based on theone or more electrical signals, the frequency of the first resonatorbeam and the frequency of the second resonator beam; and calculating, bythe processing circuitry and based on the frequency of the firstresonator beam and the frequency of the second resonator beam, anacceleration of the VBA.

In other examples, the disclosure describes system for determiningacceleration, the system comprising: processing circuitry coupled to aresonator driver circuit and configured to cause the resonator drivercircuit to output a resonator driver signal; a vibrating beamaccelerometer (VBA) device comprising a resonator configured to receivethe resonator driver signal, the resonator comprising: a resonator beam;a drive electrode; and a first sense electrode and a second senseelectrode, wherein: the first sense electrode is located on a first sideof the resonator beam, the second sense electrode is located on a secondside of the resonator beam opposite the first side such that a firstchange in capacitance with respect to displacement (dC₁/dx) for thefirst sense electrode is approximately equal in magnitude to a secondchange in capacitance with respect to displacement (dC₂/dx) for thesecond sense electrode and opposite in sign; and electrical signalrouting: comprising: a drive signal path coupled to the drive electrode;a first sense signal path coupled to the first sense electrode; and asecond sense signal path coupled to the second sense electrode, whereinthe electrical signal routing is configured to produce: a firstparasitic capacitance between the drive signal path and the first sensesignal path that generates a first parasitic feedthrough current; and asecond parasitic capacitance between the drive signal path and thesecond sense signal path, that generates a second parasitic feedthroughcurrent, such that the first parasitic feedthrough current and thesecond parasitic feedthrough current are approximately equal inmagnitude.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a conceptual diagram illustrating a pendulous VBA withsupporting flexures, X-direction resonators, and damping combs.

FIG. 2 is a conceptual diagram illustrating a sectional view of apendulous VBA with supporting flexures and with X-direction resonators.

FIG. 3A is a block diagram illustrating a system including a pendulousVBA according to one or more techniques of this disclosure.

FIG. 3B is a block diagram illustrating an accelerometer system, inaccordance with one or more techniques of this disclosure.

FIG. 4 is a conceptual diagram illustrating an example of resonatorelectrode placement and routing of electrical signals to avoid theeffects of parasitic feedthrough capacitance on accelerometerperformance.

FIGS. 5A and 5B are schematic diagrams illustrating an example MEMS VBAconfigured with a single sense electrode.

FIGS. 6A and 6B are schematic diagrams illustrating an example MEMS VBAconfigured with two sense electrodes according to one or more techniquesof this disclosure.

FIG. 7A is a conceptual diagram illustrating a first resonator withadded masses, in accordance with one or more techniques of thisdisclosure.

FIG. 7B is a conceptual diagram illustrating a portion of the firstresonator of FIG. 7A including added masses, in accordance with one ormore techniques of this disclosure.

FIG. 8A is a conceptual diagram illustrating a second resonator forminggaps, in accordance with one or more techniques of this disclosure.

FIG. 8B is a conceptual diagram illustrating a portion of secondresonator of FIG. 5A including gaps, in accordance with one or moretechniques of this disclosure.

FIG. 9 is a graph illustrating a first plot representing a quadraticnonlinearity coefficient as a function of added mass position and asecond plot representing a zero acceleration resonant frequencydifference as a function of added mass position, in accordance with oneor more techniques of this disclosure.

FIG. 10 is a flow diagram illustrating an example operation fordetermining an acceleration of a VBA, in accordance with one or moretechniques of this disclosure.

DETAILED DESCRIPTION

The techniques of this disclosure may be incorporated into a variety ofVBAs. For example, the techniques of planar geometry and a singleprimary mechanical anchor between the support base and the VBA describedby U.S. patent application Ser. No. 16/041,244, which is herebyincorporated by reference in its entirety, may be combined with thetechniques of this disclosure.

FIG. 1 is a conceptual diagram illustrating a pendulous VBA withsupporting flexures and with X-direction resonators. FIG. 1 is a topview of VBA 30 showing the anchor 14 to the support base, but thesupport base is not shown in FIG. 1. VBA 30 includes pendulous proofmass 32 connected to anchor 14 and resonator connection structure 16 athinge flexure 22, with damping combs 40 and resonators 18A and 18B. FIG.1 also shows section A-A′, which runs along the long axis of resonatorconnection structure 16 and through anchor 14. In this disclosure, theresonator connection structure 16 may also be referred to as the rigidanchor connection 16.

Pendulous proof mass 32 includes supporting flexures and connects toresonator connection structure 16 at anchor 14 by hinge flexure 22.Hinge flexure 22 suspends the proof mass at anchor 14 and the point atwhich hinge flexure 22 connects to anchor 14 is the center of rotationfor proof mass 32. Left and right resonators 18A and 18B connect to thesame primary anchor 14 by resonator connection structure 16. Resonators18A and 18B connect to proof mass 32 at a distance r1 from the center ofrotation for proof mass 12. Center of mass 24 for proof mass 12 is at adistance r2 from the center of rotation for proof mass 12. Thearrangement of VBA 30 results in the inertial force of proof mass 12 onthe released beams of resonator beams 19A and 19B amplified by theleverage ratio r2/r1.

In the example FIG. 1, VBA 30 may be implemented as an in-planemicro-electromechanical systems (MEMS) VBA. Proof mass 32 may containone or more damping combs 40 that include one or more banks of movablecomb fingers 42 attached to proof mass 32. Movable comb fingers 42 maybe interdigitated with anchored comb fingers 44 that are attached tofixed geometry, such as anchors 46. These damping comb fingers 42 and 44lie in the same plane as proof mass 32 and may provide air damping forproof mass 32 when the MEMS die is placed into a package containing apressure above a vacuum. In some examples, the MEMS die may be placedinto a ceramic package that contains an inside pressure of approximately1 Torr. Changes in pressure may change the degree of damping. In thisdisclosure, “movable comb fingers 42” may be referred to as “rotor combfingers 42.” Also, “anchored comb fingers 44” may be referred to as“stator comb fingers 44.”

In this disclosure air damping may include damping cause by two surfacessliding past each other, e.g. Couette damping. In other examples, airdamping may include two surfaces approaching each other, e.g.squeezed-film damping. In some examples, one type of air damping mayhave a greater effect that other types of air damping and may bedependent on the VBA geometry.

The geometry of the damping combs 40 may minimize the air gap andmaximize the overlap area between the movable comb fingers 42 andanchored comb fingers 44. As depicted by FIG. 1, a first comb finger ofthe movable comb fingers is adjacent to a first comb finger and a secondcomb finger of the anchored comb fingers. The overlapped portion has atotal linear distance. The total linear distance is a sum of firstlength and second length. The first length is a linear distance in whicha first edge of a first comb finger of the movable comb fingers overlapswith a first edge of a first comb finger of the anchored comb fingers.The second length is a linear distance in which a second edge of thefirst comb finger of movable comb fingers overlaps with a first edge ofa second comb finger of the anchored comb fingers. The example of FIG. 1shows six damping combs. However, in other examples, a VBA may includemore or fewer damping combs. More damping combs may result in a largeroverlapped portion and therefore a longer total linear distance. Alonger total linear distance may result in greater damping. Similarly,more fingers per damping comb may result in a longer total lineardistance and greater damping. Movable comb fingers and anchored combfingers may be configured with a variety of widths, in the X-direction.Thinner (e.g. skinnier) fingers may result in more fingers, more totallinear distance, and greater damping. Also, movable comb fingers andanchored comb fingers may be configured with a variety of lengths, inthe Y-direction. Longer fingers may result in more total linear distanceand greater damping. Because the quality factor depends on the dampingas well as the mass and stiffness of VBA 30, in selecting the geometryof the damping combs 40 a designer may consider the desired amountdamping and the mechanical and structural strength of VBA 30.

Proof mass 32 may include one or more support flexures to increasestiffness of proof mass 32 in the out-of-plane (z) direction. In otherwords, the support flexures, e.g. flexure 33, coupled to proof mass 32are configured to restrict out-of-plane motion of the pendulous proofmass with respect to the X-Y plane parallel to the proof mass 32 andresonator connection structure 16. These flexures are configured to besubstantially more flexible in the in-plane (x and y) directions thanthe rigid resonator connection structure or the axial stiffness of theresonators. For example, flexure 33 includes an anchor portion,connected to the support base (not shown in FIG. 1) similar to theprimary anchor 14 and anchors 46. Flexure 33 may include a flexibleportion 36C connected between the anchor portion 33 and proof mass 32.The flexible portion 36C may be of the same or similar material to thatof proof mass 32. The configuration of the one or more support flexuresmay reduce out of plane movement, while avoiding bias caused by forcesapplied to the accelerometer mechanism (e.g. proof mass 32 andresonators 18A and 18B) that may be caused by CTE mismatch between thesubstrate and the accelerometer mechanism.

Proof mass 32 may include additional support flexures, such as theflexures with anchor portions 34A and 34B and flexible portions 36A and36B. As described above for flexure 33, flexible portions 36A and 36Bmay be of the same or similar material to proof mass 32. The position ofanchor portions 34A and 34B and the shape and configuration of flexibleportions 36A and 36B shown in FIG. 1 is just one example technique forproviding support flexures to stiffen movement of proof mass 32 in theout-of-plane (z) direction. In other examples, flexible portions 36A and36B may have different shapes, such as a straight beam or an S-shape. Inother examples, VBA 30 may have more or fewer support flexures. Theanchor portions of support flexures of this disclosure will not exertsignificant forces on proof mass 32, so the mechanism of VBA 30 willstill be connected to the structure of the support base primarily by asingle anchor region, e.g. anchor 14. Advantages of the geometry of VBA30 may include reduced bias errors that may otherwise result from thethermal expansion mismatch between the glass substrate (support base)and the silicon mechanism (e.g. pendulous proof mass 32).

Use of a single primary mechanical anchor 14 may reduce or prevent biaserrors that can be caused by external mechanical forces applied to thecircuit board, package, and/or substrate that contains the accelerometermechanism. Since the source of these forces may be unavoidable (e.g.,thermal expansion mismatch between the substrate and mechanism), thegeometry of the VBA of this disclosure may mechanically isolate thesensitive components. Another advantage may include reduced cost andcomplexity, by achieving the mechanical isolation within the MEMSmechanism, which may avoid the need for additional manufacturing stepsor components, such as discrete isolation stages.

Damping combs 40 is one example technique to damp the proof mass motionof an accelerometer while achieving an underdamped resonator. Vibratingbeam accelerometers (VBAs) function by using a proof mass to applyinertial force to a vibrating beam, aka resonators 18A and 18B, suchthat the applied acceleration can be measured as a change in resonantfrequency of the vibrating beam.

A high quality factor may provide a benefit of mitigating the phaseshift inherent to the resonator control electronics. This phase shiftmay cause a frequency shift, which ultimately manifests as a bias error.A large quality factor (Q), i.e., substantially underdamped, also maydecrease the applied voltage necessary to achieve a certain displacementamplitude. However, to minimize vibration rectification error (VRE), themotion of the proof mass may be substantially damped, and in someexamples may be critically damped, i.e. returns an equilibrium state asquickly as possible without oscillating. Without sufficient proof massdamping, the accelerometer output may exhibit unacceptable bias errorsin the presence of environmental vibration.

In contrast to damping combs 40, the geometry of resonators 18 a and 18Bof VBA 30 of this disclosure may be designed to avoid air damping. Thegeometry and the partial pressure of the components of a MEMS VBA ofthis disclosure may enable underdamped resonators with relatively highquality-factor, Q but damp the proof mass such that the proof mass Q isrelatively low when compared to the Q of the resonators. For example, areduced total linear distance for the combs on resonators 18, whencompared with the total linear distance for damping combs 40 mayconfigure the relative Q between combs for resonators 18 and dampingcombs 40. Similarly, the air gap between the anchored and releasedportions of resonators 18, and the air gap between rotor comb fingers 42and stator comb fingers 44 of damping combs 40 also may impact therelative Q.

A quality factor Q is often assigned to a damped oscillator, where Q isthe ratio of stored energy in the oscillator to the energy dissipatedper radian. In an overdamped system, the system returns to equilibriumwithout oscillating. A critically damped system returns to equilibriumas quickly as possible without oscillating. An underdamped system mayoscillate (at reduced frequency compared to the undamped case) with theamplitude gradually decreasing to zero. The quality factor may bewritten as:

Q=E/[−dE/dθ]

When dE/dθ is written as (dE/dt)/(dθ/dt) the equation becomes:

Q=E/[−dE/dt/dθ/dt].

Since dE/dt is P, the power dissipated, and dθ/dt is the angularfrequency ω, this may be written as:

Q=ωE/[−dE/dt]=ωE/P=ω(stored energy/power dissipated).

The frequency may be further described as: ω₁ is the underdampedoscillation frequency (slightly smaller than the undamped frequencyω_(o)): ω₁ ²=ω_(o) ²−β².

The techniques of this disclosure may be applied, for example, tomicro-electromechanical systems (MEMS) vibrating beam accelerometers(VBAs), which represents one of multiple possibilities capable ofachieving the required accelerometer performance. The techniques of thisdisclosure may improve the basic operation of a VBA. In existing MEMSVBAs, the resonator may be substantially underdamped (with Q's rangingfrom 100's to potentially 100,000's), which may reduce the effects ofthe phase shift from the control electronics on the closed-loop resonantfrequency. An underdamped resonator contrasts with a second design goalof damping the proof mass, as discussed above. These techniques mayprovide a means to achieve an underdamped resonator (Q˜1000's) whilealso damping the proof mass, which represents an advantage over otheralternative solutions.

Alternative solutions exist for proof mass partial damping, but somealternatives have disadvantages that limit the required combination ofperformance, cost, and size, weight, and power (SWaP). A firstalternative example may include sealing both the proof mass andresonator at full atmosphere. The full atmosphere solution may work forlarger devices. But air damping of the resonator becomes excessive afterscaling dimensions down to typical MEMS scale. Excessive air damping maylimit the capabilities of the electrostatic drive and increase thedevice's susceptibility to phase errors from the control electronics.

A second alternative example may include sealing the proof mass andresonator in separate cavities such that proof mass is packaged at fullatmosphere while the resonator is packaged at vacuum. This alternativemay significantly complicate device fabrication, and therefore mayultimately increase cost.

A third alternative example may include sealing the proof mass andresonator at vacuum. The third alternative may mitigate vibrationrectification error by setting the proof mass resonant frequency to besubstantially higher than environmental vibration frequencies.Unfortunately, the available die size and minimum resonator beam widthdimensions may prevent this solution from being feasible. Under thecurrent constraints, substantially increasing the proof mass frequencymay result in a low scale factor, which could ultimately cause poor biasperformance.

A fourth example may include sealing the proof mass and resonator atvacuum. Force rebalance actuators that actively suppress vibration maymitigate vibration rectification error. Additional actuation electrodescould be included to counteract vibration at high frequencies (>100 Hz)while allowing the proof mass to deflect at lower frequencies (<100 Hz).This solution may be feasible but introduces additional complexity, andpresumably cost, to both the mechanical device and supportingelectronics.

The techniques of this disclosure, compared to prior art techniques, mayprovide a means to damp the proof mass while leaving the resonatorssignificantly underdamped. This damping is achieved through gas dampingwithout requiring separate cavities for different pressures. Ultimately,the techniques of this disclosure may enable navigation-gradeaccelerometers with reduced cost and SWaP to maintain bias repeatabilityin the presence of environmental vibration. These techniques may avoidseparate pressure cavities and/or more complicated supportingelectronics, both of which can lead to higher cost.

Use of partial pressure damping may include integrating the followingfeatures into a VBA design:

-   -   1. The proof mass may have large portions of area that define a        small air gap (typically on the order of microns) between the        proof mass and anchored geometry. Given sufficient gas pressure,        this gap may generate air damping and ultimately reduce the Q of        the proof mass motion.    -   2. The resonator may have only small portions of area that        contribute to air damping, which may enable relatively high-Q        resonator.    -   3. The MEMS device may be packaged at a partial pressure that,        in conjunction with the proof mass damping, results in        relatively high-Q resonator (Q˜100's or higher) and a low-Q        proof mass (Q<100).

In some examples, the partial pressure techniques may be implementedwithin an in-plane MEMS VBA. As shown in FIG. 1, proof mass 32 thatincludes banks of movable comb fingers 42 interdigitated with anchoredcomb fingers 44 may be attached to fixed geometry portions 46 of theaccelerometer. These damping comb 40 fingers provide air damping forproof mass 32. To maximize damping, the air gap may be reduced while theoverlap area between the comb fingers 42 and 44 is maximized. Unlike thedamping combs, the resonator may be configured to avoid air damping. TheMEMS die is placed into a ceramic package that contains a pressure ofapproximately 1 Torr. This partial pressure may enable resonators withrelatively high Q (˜1000) but keeps the proof mass Q somewhat damped(Q˜10's).

In addition to an in-plane MEMS VBA, the same concept can be applied toan out-of-plane MEMS VBA. Such a device may use a parallel plate gapbetween the proof mass and anchored geometry instead of interdigitatedcomb fingers. The underlying concept may be the same, that is, airdamping would damp the proof mass while leaving the resonators withrelatively high Q. A similar partial pressure on the order of 1 Torrwould likely result in sufficient damping with typical air gaps anddevice geometry.

Note that the techniques of this disclosure can apply to VBAs operatingby different methods of actuation. For example, piezo-electric actuationof the resonators could alleviate the need for small capacitive air gapswithin the resonator geometry. Larger capacitive air gaps could enablean even larger differences between the resonator Q and the proof mass Q.In some examples, VBAs may provide proof mass damping via banks ofdamping combs embedded within the proof mass, but other geometries andconfigurations could theoretically achieve a similar effect. In someexamples, damping combs may be attached to the sides of the proof massrather than being embedded in the middle. For some designs, merely theedge of the proof mass itself with a sufficiently small air gap might beenough to provide proof mass damping.

FIG. 2 is a conceptual diagram illustrating a sectional view of apendulous VBA with supporting flexures and with X-direction resonators.FIG. 2 shows section A-A′ of VBA 30 depicted in FIG. 1, which runs downthe long axis of resonator connection structure 16 and through anchor14. Items in FIG. 2 with the same reference numbers as in FIG. 1 havethe same description, properties, and function as described above. Forexample, VBA 50 includes pendulous proof mass 32 (not shown in FIG. 2)connected to resonator connection structure 16 at anchor 14. FIG. 2 alsoshows the anchor portion of anchored combs 26C and 20C, as well as theanchored portions of the support flexures, 34A and 34B. Anchors 46 fordamping combs 40 may also be mechanically connected to support base 36(not shown in FIG. 2).

As with VBA 30 described above in relation to FIG. 1, VBA 50 may befabricated using silicon and glass masks such that both the proof mass32 and resonator connection structure 16 are primarily anchored to asingle region, e.g. at anchor 14. The released silicon mechanicalstructure of VBA 50 may be tethered to support base 36, which may be aglass substrate, such as quartz substrate or a silicon substrate. Proofmass 32 may be also tethered at other anchor regions, e.g. anchorportions 34A and 34B, configured to allow the released silicon portions,such as proof mass 32 and the resonator beams 19A and 19B of resonators18A and 18B (not shown in FIG. 2) to move freely relative to the supportbase 36.

Support base 36 may include enclosing structures, such as structures 38Aand 38B, which may surround the released portions of VBA 30. In someexamples, VBA 30 may include both lower support base 36 and an uppersupport (not shown in FIG. 2). In some examples the anchored portions,e.g. anchor 14, may be mechanically connected to both the lower supportbase 36 and the upper support. Support base 36 may define a secondplane, also substantially parallel to the X-Y plane that is differentfrom the plane of the released portions of VBA 30. The plane defined bythe released portions of VBA 30 (e.g. resonator beams 19A-19B and proofmass 32) may be substantially parallel to the second plane defined bysupport base 36. As described above in relation to FIG. 1, air gapsbetween the plane of the proof mass and the plane of support base 36 mayallow the silicon portions, such as the proof mass, to move freelyrelative to the substrate.

Resonator connection structure 16 may be configured to be more rigidthan the resonators. The rigid structure of resonator connectionstructure 16 connects to the resonators and branches back to the primarymechanical anchor 14, which is connected to support base 36. Resonatorconnection structure 16, as described above, may be sized to be stifferthan the axial spring constant of the resonators and supports theresonators in the in-plane (e.g. x and y) directions. In some examples,resonator connection structure 16 may be an order of magnitude stifferthan resonator beams 19A-19B. The single primary anchor 14 allows themechanical connections of the released portions of VBA 30 to thermallyexpand at a different rate or direction of the support base 36 withoutbeing restrained by other connections to support base 36 that may causebias and inaccuracy.

Support base 36 may include metal layers deposited onto the glasssubstrates (not shown in FIG. 2), which define electrical wires thatconnect silicon electrodes to wire bond pads. In some examples, supportbase 36 may include bond pads and other metal structures on the bottomsurface of support base 36 (e.g. as indicated by the arrow from 36),such as conductive paths 37A and 37B. In some examples, support base 36may include metal layers on the top surface, e.g. on the surfaceopposite the bottom surface, and in other examples, support base 36 mayinclude intermediate metal layers between the top and bottom surfaces(not shown in FIG. 2). In some examples the metal layers mayelectrically connect to each other with vias, or other types ofconnections through support base 36. In some examples, electrical wiresmay also be defined with other conductive material other than metal. Asdescribed above in relation to FIG. 1, the metal layers, or otherconductive material, may define electrical paths to carry signals to andfrom VBA 30, such as conductive paths 37A and 37B.

As described above in relation to FIG. 1, each resonator of the one ormore resonators may include a resonator beam with released comb (e.g.19A) and an anchored comb (e.g. 20C and 26C). As shown in FIG. 2, theanchor portion of anchored combs 20C and 26C extend from the plane ofsupport base 36 to the plane of the released portions of VBA 30. Thecomb portions of anchored combs 20C and 26C are supported in the sameplane as resonator beams 19A-19B and proof mass 12 and 32, describedabove in relation to FIG. 1.

FIG. 3A is a functional block diagram illustrating a system including apendulous VBA according to one or more techniques of this disclosure.The functional blocks of system 100 are just one example of a systemthat may include a VBA according to this disclosure. In other examples,functional blocks may be combined, or functions may be grouped in adifferent manner than depicted in FIG. 3A. Other circuitry 113 mayinclude power supply circuits and other processing circuits that may usethe output of accelerometer 110 to perform various functions, e.g.inertial navigation, and motion sensing.

System 100 may include processing circuitry 102, resonator drivercircuits 104A and 104B, and accelerometer 110. Accelerometer 110 mayinclude any VBA, including the pendulous proof mass VBA accelerometersdescribed above in relation to FIGS. 1-4B.

In the example of FIG. 3A, resonator driver circuits 104A and 104B areoperatively connected to accelerometer 110 and may send drive signals106A and 106B to accelerometer 110 as well as receive sense signals 108Aand 108B from accelerometer 110. In the example of FIG. 3A, resonatordriver circuit 104A may be coupled to one resonator, e.g. resonator 18Adepicted in FIG. 1, and resonator driver circuit 104B may be coupled toa second resonator, e.g. resonator 18B. Resonator driver circuits 104Aand 104B may be configured to output a signal that causes the resonatorsof accelerometer 110 to vibrate at a respective resonant frequency ofeach of the resonators. In some examples, vibrate means to excite andsustain mechanical motion for each resonator through electrostaticactuation. In some examples, resonator driver circuits 104A and 104B mayinclude one or more oscillator circuits. In some examples the signal toaccelerometer 110 may travel along conductive pathways along or withinthe support base of accelerometer, such as support base 36 describedabove in relation to FIG. 2. The signal from resonator driver circuits104A and 104B may provide a patterned electric field to cause resonatorsof accelerometer 110 to maintain resonance. Processing circuitry 102 incombination with resonator driver circuits 104A and 104B may be anexample of the control electronics described above in relation to FIG.1.

Resonator driver circuit 104A may output drive signal 106A at adifferent frequency than drive signal 106B from resonator driver circuit104B. The example of FIG. 3A may be configured to determine adifferential frequency signal based on sense signals 108A and 108B.Resonator driver circuits 104A and 104B may adjust the output of drivesignals 106A and 106B based on the feedback loop from sense signals 108Aand 108B, e.g. to maintain the resonators at the respective resonantfrequency. As described above, a VBA according to this disclosure mayinclude one resonator or more than two resonators and may also includefewer or additional resonator driver circuits.

In this disclosure, a “differential frequency” measurement may includecombinations of frequencies beyond a simple subtraction. In someexamples an output of a first resonator may be weighted differently thanthe output of a second or third resonator as part of the differentialfrequency measurement. For example, a first resonator may be weighted to98% of the resonator output as part of determining the differentialfrequency measurement compared to other resonators. In other examples,the output of each resonator may be squared, or otherwise processed, aspart of determining the differential frequency measurement. In otherexamples any combination of weighting, square, square root, inversion,or other processing may be part of determining the differentialfrequency measurement.

As described above in relation to FIGS. 1 and 2, an acceleration of thependulous mass VBA, e.g. in a direction substantially parallel to theplane of the proof mass, may cause a rotation of the pendulous proofmass about the hinge flexure parallel to the plane of the proof mass.The resonators of accelerometer 110 may be configured to receive aforce, in response to the rotation of the proof mass, such that theforce causes the resonator to flex in the plane of the proof mass andcause a respective change in resonant frequency of at least oneresonator.

Processing circuitry 102 may communicate with resonator driver circuits104A and 104B. Processing circuitry 102 may include various signalprocessing functions, such as filtering, amplification, andanalog-to-digital conversion (ADC). Filtering functions may includehigh-pass, band-pass, or other types of signal filtering. In someexamples, resonator driver circuits 104A and 104B may also includesignal processing functions, such as amplification and filtering.Processing circuitry 102 may output the processed signal received fromaccelerometer 110 to other circuitry 113 as an analog or digital signal.Processing circuitry 102 may also receive signals from other circuitry113, such as command signals, calibration signals and similar signals.

Processing circuitry 102 may operatively connect to accelerometer 110,e.g. via resonator driver circuits 104A and 104B. Processing circuitry102 may be configured to receive the signal from accelerometer 110,which may indicate of a respective change in the resonant frequency ofat least one resonator of accelerometer 110. Based on the respectivechange in resonant frequency, processing circuitry 102 may determine anacceleration measurement. In other examples (not shown in FIG. 3A),processing circuitry 102 may be part of the feedback loop fromaccelerometer 110 and may control the drive signals 106A and 106B tosustain the motion of the resonators at their resonant frequency.

FIG. 3B is a block diagram illustrating an accelerometer system 101, inaccordance with one or more techniques of this disclosure. Asillustrated in FIG. 3B, accelerometer system 101 includes processingcircuitry 103, resonator driver circuits 105A-105B (collectively,“resonator driver circuits 105”), and proof mass assembly 111. Proofmass assembly 111 includes proof mass 112, resonator connectionstructure 116, first resonator 120, and second resonator 130. Firstresonator 120 includes first mechanical beam 124A and second mechanicalbeam 124B (collectively, “mechanical beams 124”), and first set ofelectrodes 128A, second set of electrodes 128B, and third set ofelectrodes 128C (collectively, “electrodes 128”). Second resonator 130includes third mechanical beam 134A and fourth mechanical beam 134B(collectively, “mechanical beams 134”), and fourth set of electrodes138A, fifth set of electrodes 138B, and sixth set of electrodes 138C(collectively, “electrodes 138”).

Accelerometer system 101 may, in some examples, be configured todetermine an acceleration associated with an object (not illustrated inFIG. 3B) based on a measured vibration frequency of one or both of firstresonator 120 and second resonator 130 which are connected to proof mass112. In some cases, the vibration of first resonator 120 and secondresonator 130 is induced by drive signals emitted by resonator drivercircuit 105A and resonator driver circuit 105B, respectively. In turn,first resonator 120 may output a first set of sense signals and secondresonator 130 may output a second set of sense signals and processingcircuitry 103 may determine an acceleration of the object based on thefirst set of sense signals and the second set of sense signals.

Processing circuitry 103, in some examples, may include one or moreprocessors that are configured to implement functionality and/or processinstructions for execution within accelerometer system 101. For example,processing circuitry 103 may be capable of processing instructionsstored in a storage device. Processing circuitry 103 may include, forexample, microprocessors, digital signal processors (DSPs), applicationspecific integrated circuits (ASICs), field-programmable gate arrays(FPGAs), or equivalent discrete or integrated logic circuitry, or acombination of any of the foregoing devices or circuitry. Accordingly,processing circuitry 103 may include any suitable structure, whether inhardware, software, firmware, or any combination thereof, to perform thefunctions ascribed herein to processing circuitry 103.

A memory (not illustrated in FIG. 3B) may be configured to storeinformation within accelerometer system 101 during operation. The memorymay include a computer-readable storage medium or computer-readablestorage device. In some examples, the memory includes one or more of ashort-term memory or a long-term memory. The memory may include, forexample, random access memories (RAM), dynamic random access memories(DRAM), static random access memories (SRAM), magnetic discs, opticaldiscs, flash memories, or forms of electrically programmable memories(EPROM) or electrically erasable and programmable memories (EEPROM). Insome examples, the memory is used to store program instructions forexecution by processing circuitry 103.

In some examples, resonator driver circuit 105A may be electricallycoupled to first resonator 120. Resonator driver circuit 105A may outputa first set of drive signals to first resonator 120, causing firstresonator 120 to vibrate at a resonant frequency. Additionally, in someexamples, resonator driver circuit 105A may receive a first set of sensesignals from first resonator 120, where the first set of sense signalsmay be indicative of a mechanical vibration frequency of first resonator120. Resonator driver circuit 105A may output the first set of sensesignals to processing circuitry 103 for analysis. In some examples, thefirst set of sense signals may represent a stream of data such thatprocessing circuitry 103 may determine the mechanical vibrationfrequency of first resonator 120 in real-time or near real-time.

In some examples, resonator driver circuit 105B may be electricallycoupled to second resonator 130. Resonator driver circuit 105B mayoutput a second set of drive signals to second resonator 130, causingsecond resonator 130 to vibrate at a resonant frequency. Additionally,in some examples, resonator driver circuit 105B may receive a second setof sense signals from second resonator 130, where the second set ofsense signals may be indicative of a mechanical vibration frequency offirst resonator 130. Resonator driver circuit 105B may output the secondset of sense signals to processing circuitry 103 for analysis. In someexamples, the second set of sense signals may represent a stream of datasuch that processing circuitry 103 may determine the mechanicalvibration frequency of second resonator 130 in real-time or nearreal-time.

Proof mass assembly 111 may secure proof mass 112 to resonatorconnection structure 116 using first resonator 120 and second resonator130. For example, Proof mass 112 may be secured to resonator connectionstructure 116 in a first direction with hinge flexure 114. Proof mass112 may be secured to resonator connection structure 116 in a seconddirection with first resonator 120 and resonator 130. Proof mass 112 maybe configured to pivot about hinge flexure 114, applying pressure tofirst resonator 120 and second resonator 130 in the second direction.For example, if proof mass 112 pivots towards first resonator 120, proofmass 112 applies a compression force to first resonator 120 and appliesa tension force to second resonator 130. If proof mass 112 pivotstowards second resonator 130, proof mass 112 applies a tension force tofirst resonator 120 and applies a compression force to second resonator130.

An acceleration of proof mass assembly 111 may affect a degree to whichproof mass 112 pivots about hinge flexure 114. As such, the accelerationof proof mass assembly 111 may determine an amount of force applied tofirst resonator 120 and an amount of force applied to second resonator130. An amount of force (e.g., compression force or tension force)applied to resonators 120, 130 may be correlated with an accelerationvector of proof amass assembly 111, where the acceleration vector isnormal to hinge flexure 114.

In some examples, the amount of force applied to first resonator 120 maybe correlated with a resonant frequency in which first resonator 120vibrates in response to resonator driver circuit 105A outputting thefirst set of drive signals to first resonator 120. For example, firstresonator 120 may include mechanical beams 124. In this way, firstresonator 120 may represent a double-ended tuning fork (DETF) structure,where each mechanical beam of mechanical beams 124 vibrate at theresonant frequency in response to receiving the first set of drivesignals. Electrodes 128 may generate electrical signals indicative of amechanical vibration frequency of first mechanical beam 124A and amechanical vibration frequency of second mechanical beam 124B. Forexample, the first set of electrodes 128A may generate a firstelectrical signal, the second set of electrodes 128B may generate asecond electrical signal, and the third set of electrodes 128C maygenerate a third electrical signal. Electrodes 128 may output the firstelectrical signal, the second electrical signal, and the thirdelectrical signal to processing circuitry 103.

Processing circuitry 103 may determine a difference between the firstelectrical signal and the second electrical signal and determine themechanical vibration frequency of first mechanical beam 124A based onthe difference between the first electrical signal and the secondelectrical signal. Additionally, or alternatively, processing circuitry103 may determine a difference between the second electrical signal andthe third electrical signal and determine the mechanical vibrationfrequency of second mechanical beam 124B based on the difference betweenthe second electrical signal and the third electrical signal. In someexamples, the mechanical vibration frequency of the first mechanicalbeam 124A and the second mechanical beam 124B are substantially the samewhen resonator driver circuit 105A outputs the first set of drivesignals to first resonator 120. For example, the mechanical vibrationfrequency of first mechanical beam 124A and the mechanical vibrationfrequency of second mechanical beam 124B may both represent the resonantfrequency of first resonator 120, where the resonant frequency iscorrelated with an amount of force applied to first resonator 120 byproof mass 112. The amount of force that proof mass 112 applies to firstresonator 120 may be correlated with an acceleration of proof massassembly 111 relative to a long axis of resonator connection structure116. As such, processing circuitry 103 may calculate the acceleration ofproof mass 112 relative to the long axis of resonator connectionstructure 116 based on the detected mechanical vibration frequency ofmechanical beams 124.

In some examples, the amount of force applied to second resonator 130may be correlated with a resonant frequency in which second resonator130 vibrates in response to resonator driver circuit 105B outputting thesecond set of drive signals to second resonator 130. For example, secondresonator 130 may include mechanical beams 134. In this way, secondresonator 130 may represent a double-ended tuning fork (DETF) structure,where each mechanical beam of mechanical beams 134 vibrate at theresonant frequency in response to receiving the second set of drivesignals. Electrodes 138 may generate electrical signals indicative of amechanical vibration frequency of third mechanical beam 134A and amechanical vibration frequency of fourth mechanical beam 134B. Forexample, the fourth set of electrodes 138A may generate a fourthelectrical signal, the fifth set of electrodes 138B may generate a fifthelectrical signal, and the sixth set of electrodes 138C may generate asixth electrical signal. Electrodes 138 may output the fourth electricalsignal, the fifth electrical signal, and the sixth electrical signal toprocessing circuitry 103.

Processing circuitry 103 may determine a difference between the fourthelectrical signal and the fifth electrical signal and determine themechanical vibration frequency of third mechanical beam 134A based onthe difference between the fourth electrical signal and the fifthelectrical signal. Additionally, or alternatively, processing circuitry103 may determine a difference between the fifth electrical signal andthe sixth electrical signal and determine the mechanical vibrationfrequency of fourth mechanical beam 134B based on the difference betweenthe fifth electrical signal and the sixth electrical signal. In someexamples, the mechanical vibration frequency of the third mechanicalbeam 134A and the fourth mechanical beam 134B are substantially the samewhen resonator driver circuit 105B outputs the second set of drivesignals to second resonator 130. For example, the mechanical vibrationfrequency of third mechanical beam 134A and the mechanical vibrationfrequency of fourth mechanical beam 134B may both represent the resonantfrequency of second resonator 130, where the resonant frequency iscorrelated with an amount of force applied to second resonator 130 byproof mass 112. The amount of force that proof mass 112 applies tosecond resonator 130 may be correlated with an acceleration of proofmass assembly 111 relative to a long axis of resonator connectionstructure 116. As such, processing circuitry 103 may calculate theacceleration of proof mass 112 relative to the long axis of resonatorconnection structure 116 based on the detected mechanical vibrationfrequency of mechanical beams 134.

In some cases, processing circuitry 103 may calculate an acceleration ofproof mass assembly 111 relative to the long axis of resonatorconnection structure 116 based on a difference between the detectedmechanical vibration frequency of mechanical beams 124 and the detectedmechanical vibration frequency of mechanical beams 134. When proof massassembly 111 accelerates in a first direction along the long axis ofresonator connection structure 116, proof mass 112 pivots towards firstresonator 120, causing proof mass 112 to apply a compression force tofirst resonator 120 and apply a tension force to second resonator 130.When proof mass assembly 111 accelerates in a second direction along thelong axis of resonator connection structure 116, proof mass 112 pivotstowards second resonator 130, causing proof mass 112 to apply a tensionforce to first resonator 120 and apply a compression force to secondresonator 130. A resonant frequency of a resonator which is applied afirst compression force may be greater than a resonant frequency of theresonator which is applied a second compression force, when the firstcompression force is less than the second compression force. A resonantfrequency of a resonator which is applied a first tension force may begreater than a resonant frequency of the resonator which is applied asecond tension force, when the first tension force is greater than thesecond tension force.

Although accelerometer system 101 is illustrated as including resonatorconnection structure 116, in some examples not illustrated in FIG. 3B,proof mass 112, first resonator 120, and second resonator 130 are notconnected to a resonator connection structure. In some such examples,proof mass 112, first resonator 120, and second resonator 130 areconnected to a substrate. For example, hinge flexure 114 may fix proofmass 112 to the substrate such that proof mass 112 may pivot about hingeflexure 114, exerting tension forces and/or compression forces on firstresonator 120 and second resonator 130.

In some examples, the difference between the resonant frequency of firstresonator 120 and the resonant frequency of second resonator 130 mayhave a near linear relationship with the acceleration proof massassembly 111. In some examples, the relationship between the differencein resonant frequencies of resonators 120, 130 and the acceleration ofproof mass assembly 111 might not be perfectly linear. For example, therelationship may include a quadratic nonlinearity coefficient (K₂)representing a nonlinearity in the relationship between the differencein the resonant frequencies of resonators 120, 130 and the accelerationof proof mass assembly 111. It may be beneficial for the quadraticnonlinearity coefficient to be zero or close to zero so that processingcircuitry 103 is configured to accurately determine the acceleration ofproof mass assembly 111 based on the relationship between the differencein resonant frequencies of resonators 120, 130 and the acceleration ofproof mass assembly 111. One type of error is as vibration rectificationerror (VRE). VRE may be as a change in zero-g output, or accelerometerbias, that occurs during vibration. VRE may be caused by nonlinearity inan accelerometer input-to-output transfer function. Typically, the mostdominant source is the quadratic nonlinearity coefficient (K₂). In orderto avoid VRE, it may be beneficial to mitigate this quadraticnonlinearity.

Additionally, it may be beneficial for a difference between the resonantfrequency of first resonator 120 and the resonant frequency of secondresonator 130 to be nonzero while an acceleration of proof mass assembly111 is zero m/s². It may be beneficial for the difference in respectiveresonant frequencies of resonators 120, 130 to be nonzero while proofmass assembly 111 is not accelerating in order to decrease aninterference between first resonator 120 and second resonator 130 ascompared with systems in which a difference, at zero acceleration, inrespective resonant frequencies of a first resonator and a secondresonator is zero or closer to zero than the system described herein.

In some examples, accelerometer system 101 may ensure that the quadraticnonlinearity coefficient is close to zero and ensure that thezero-acceleration difference in the respective resonant frequencies ofresonators 120, 130 is nonzero by including added masses on firstresonator 120. For example, first mechanical beam 124A and secondmechanical beam 124B may each include one or more added masses, wherethe one or more added masses affect the resonant frequency of firstresonator 120 and the quadratic nonlinearity coefficient. Thirdmechanical beam 134A and fourth mechanical beam 134B may each form a oneor more gaps where the added masses are located on first mechanical beam124A and second mechanical beam 124B. In some examples, first resonator120 and second resonator 130 are substantially the same except thatfirst resonator 120 includes the added mass on first mechanical beam124A and the added mass on second mechanical beam 124B, where thirdmechanical beam 134A includes a gap corresponding to the added mass onfirst mechanical beam 124A and fourth mechanical beam 134B includes agap corresponding to the added mass on second mechanical beam 124B. Suchdifferences between the first resonator 120 and the second resonator 130may ensure that the quadratic nonlinearity coefficient is close to zero(e.g., less than 5 μg/g²) and ensure that the zero-accelerationdifference in the respective resonant frequencies of resonators 120, 130is nonzero.

For VBAs with two identical resonators, even-order nonlinearities (e.g.,quadratic nonlinearities, 4^(th) order nonlinearities) are common-modeerror sources nominally eliminated by differential output. However,mismatched resonators, such as first resonator 120 and second resonator130, may results in an accelerometer K₂ that is not necessarily set tozero. Mismatched resonators may be desirable to avoid operating bothresonators at the same frequency. Driving two resonators at similarfrequencies may cause the resonators to interfere with each other(mechanically and electrically), which ultimately degrades the output ofthe VBA. Resonators 120 and 130 may ensure that K₂ is zero or close tozero and mitigate such interference which degrades the output of theVBA.

Although accelerometer system 101 is described as having two resonators,in other examples not illustrated in FIG. 3B, an accelerometer systemmay include less than two resonators or greater than two resonators. Forexample, an accelerometer system may include one resonator. Anotheraccelerometer system may include four resonators.

FIG. 4 is a conceptual diagram illustrating an example of resonatorelectrode placement and routing of electrical signals to avoid theeffects of parasitic feedthrough capacitance on accelerometerperformance. VBA 830 is an example of VBA 30, VBA 50 and VBA 430described above in relation to FIGS. 1, 2 and 4. Pendulous proof mass832, resonator 818, resonator beam 819, flexure 833 and mechanicalanchor 814, are examples of proof mass 32, resonators 18A and 18B,resonator beams 19A and 19B, flexure 33 and mechanical anchor 14described above in relation to FIGS. 1 and 4 and therefore may have thesame description, properties and function as described above. Theexample of VBA 830 in FIG. 4 includes damping combs 840. However, inother examples, VBA 830 may have no damping combs 840.

The electrodes and routing within both the electronics and VBA mechanismmay create some parasitic capacitance between the drive electrodes andsense electrodes. The example of VBA 830 includes resonator electrodes,such as drive electrodes 838 and 839, configured to mitigate the effectsof p parasitic capacitance inherent to the VBA resonator. In thismanner, provided the feedthrough capacitances between each driveelectrode and the sense electrode are similar, the feedthrough currentswill be out-of-phase with each other resulting in zero net current.

Control electronics may connect with resonator drive electrodes, such asdrive electrode 838 and 839 to sustain motion of the vibrating beam 819.The electrodes and routing within both the electronics and VBA mechanismmay create some parasitic capacitance between the drive electrodes andsense electrodes. In the example of FIG. 4, the two different driveelectrodes 838 and 839 may receive voltage signals of opposite polarity.Drive electrodes 838 and 839 may be located on both sides of the movingMEMS element, e.g. resonator 818, such that the actuators can push andpull to drive resonator 818. In some examples, drive signals of opposingphase may be generated by analog electronics within control electronicsof the VBA. In this manner, provided the feedthrough capacitancesbetween each drive electrode and the sense electrode are similar, thefeedthrough currents will be out-of-phase with each other resulting inzero net current.

In some alternative examples, such as a configuration with a singledrive and sense electrode, this parasitic feedthrough capacitance maylead to a feedthrough current between the drive electrode and senseelectrodes. The feedthrough current may be summed with motional currentcaused by motion of the mechanical resonator. This total output currentis read by the front-end electronics and ultimately used to sustain andsense the frequency of mechanical oscillation. Therefore, thefeedthrough current caused by feedthrough capacitance may impact theresonator transfer function and the operation of the VBA.

For moderate feedthrough capacitances, the magnitude and phase of theresonator transfer function may be degraded, which may cause increasedaccelerometer noise. Stability of the accelerometer bias may be degradedif the resonator is driven too far away from mechanical resonance, sincethe resonator frequency will be more susceptible to any phase shift inthe electronics. Thus, avoiding the effect of this parasitic feedthroughcapacitance to may ultimately improve accelerometer performance.

The techniques of this disclosure may include configuring the capacitivecomb fingers of resonators 818 into discreet electrodes that includedrive electrodes 838 and 839 and two sense electrodes, sense− 856 andsense+ 858. Sense electrodes, sense− 856 and sense+ 858 may be coupledto the anchored portion of resonator 818. Furthermore, the routing ofelectrical signals 850, 852 and 854 on the die and on the analogelectronics board may be configured to produce parasitic feedthroughcapacitances, Cf+ and Cf−, that are approximately equal. In someexamples, one or more of the electrical signals may include additionalrouting 824 to ensure that the parasitic feedthrough capacitances, Cf+and Cf−, are approximately equal. Electrical signals 850, 852 and 854may connect to terminals such as drive 820, sense− 802 and sense+ 810,respectively.

The two sense electrodes on the VBA may be placed on opposite sides ofthe moving MEMS resonator beams 819 such that the changes in capacitancewith respect to displacement (dCs/dx's) are approximately equal inmagnitude and opposite in sign. Then, the sense currents (i_(s)+ andi_(s)−) will be opposite in sign, but the feedthrough currents (i_(f)+and i_(f)−) will be of the same sign. The sense outputs 802 and 810 mayconnect to a differential front-end amplifier, such as a transimpedanceor charge amplifier, which processes the difference in output currents.In this manner the feedthrough currents approximately cancel each other,and the effects may be mitigated.

Alternative solutions may exist to avoid feedthrough capacitanceeffects, but those alternatives involve additional electronicscomplexity, which is likely to increase cost. Some example alternativesmay include to drive the resonator using a sinusoidal voltage at halfthe frequency of mechanical resonance. Since electrostatic force isproportional to the square of the voltage, electrostatic actuators cancreate force at twice the frequency of the sinusoidal voltage. Providedthe second harmonic content of the drive signal is small, thisalternative solution may eliminate the possibility for drive-to-sensecapacitive feedthrough since the drive and sense signals are ofdifferent frequencies. However, this alternative solution would likelyuse a microcontroller within the resonator feedback loop. Adding adigital microcontroller would likely result in an accelerometer that issubstantially larger and more expensive than an accelerometer with ananalog control loop.

Another alternative example may use two different sense electrodesbiased with voltages of opposite polarity. Then, the resulting outputcurrents can be differenced to eliminate the effect of feedthroughcapacitance. However, sense electrodes with opposite polarity may havethe disadvantage of requiring two large bias voltages instead of justone large bias voltage.

A third alternative may use two different drive electrodes receivingvoltage signals of opposite phase. Provided the feedthrough capacitancesbetween each drive electrode and the sense electrode are similar, thefeedthrough currents will be out-of-phase with each other resulting inzero net current. This configuration requires drive electrodes on bothsides of the moving MEMS element so that the actuators can push and pullto drive the resonator. Drive signals of opposing phase may be generatedby the analog electronics and may have a disadvantage of requiring twoseparate drive circuits.

Measured test results of the resonator configuration techniques of thisdisclosure show improvement of the open-loop phase response of theanalog electronics, which is expected to improve noise and, in someexamples, improve bias stability. These techniques may be uniquecompared to other example techniques because in some examples VBAstypically use one drive and one sense electrode for each resonator.Given a one drive and one sense configuration, there is no means tocancel any feedthrough capacitance that might occur. Rather, otherexamples may simply attempt to minimize that capacitance.

The technical benefit of the techniques of this disclosure may eliminateor reduce the effect of drive-to-sense feedthrough capacitance. Thereduced capacitance may improve the open-loop phase response of theresonator in conjunction with the electronics, which, in turn, enablesthe electronics to drive the resonator directly at mechanical resonance.In some examples, these techniques may make the accelerometer deviceeasier to integrate with small variances in electronics, whichultimately relaxes requirements on the electronics themselves. Also,prior to development of the read-out electronics, there may have beensome concern that this feedthrough capacitance would be detrimental toelectronics performance. A read-out circuit is a circuit which may beconfigured to convert the information on the variation in capacitancecaused by an external acceleration into a voltage signal. Testmeasurements show that cancellation of these feedthrough currents mayresult in improvements in the open-loop response of the resonators.

The techniques of this disclosure to cancel feedthrough currents may beincorporated into a MEMS VBA. Each resonator 818 may have electrodeswired to its corresponding bond pads. The input to each resonator 818may be a single drive voltage while the outputs may be configured as twosense electrodes 841 and 842 that contain nominally out-of-phasecurrents representing physical motion of the MEMS resonators.

In the example of double-ended tuning fork resonators, each resonatorhas two moving components that oscillate in opposite directions. Driveelectrodes, e.g. drive electrodes 838 and 839, may supply a drivevoltage that excites mechanical motion at resonance. VBA 830 may includeadditional drive electrodes not shown in FIG. 4. Positive senseelectrodes, e.g. 858, may produce positive current when the tworesonator tines move apart. Negative sense electrodes, e.g. 856 mayproduce positive current when the two resonator tines move together.Thus, the sense electrodes are oriented to have dC/dx's of similarmagnitude but opposite sign. Routing of electrical signals 850, 852 and854 on the MEMS die may be configured to have similar feedthroughcapacitance between the drive and sense electrodes.

FIGS. 5A and 5B are schematic diagrams illustrating an example MEMS VBAconfigured with a single sense electrode. FIG. 5A shows a mechanicalmodel of an example single sense electrode VBA and FIG. 5B shows theequivalent electrical circuit.

In the example of FIG. 5A, DC bias voltage Vb 902 connects to a MEMSelectrode at mass 910, where mass 910 represents the mass of a resonatorbeam, not the proof mass of the VBA. Mass 910 connects to attachmentpoint 922 through a spring 916 with spring constant K, to attachmentpoint 923 through variable drive capacitance Cd 912 and to attachmentpoint 924 through variable sense capacitance Cs 914. As described abovein relation for example to FIG. 1, the capacitance may change as theresonator tines for the released region moves relative to the resonatortines for the anchored region.

AC drive voltage Vd 904 connects to a drive electrode at attachmentpoint 923 to excite mechanical motion in the resonator and cause mass910 to move along the X-axis 918. As described above in relation to FIG.4, electrodes position and signal routing may create some parasiticcapacitance, e.g. feedthrough capacitance Cf 908 between the driveelectrodes and sense electrodes. In the example configuration ofresonator 900, with a single drive and sense electrode, this parasiticfeedthrough capacitance Cf 908 may lead to a feedthrough current betweenthe drive electrode and sense electrodes that may be received by anamplifier connected to the VBA.

Circuit 950 in the example of FIG. 5B is an equivalent circuit ofresonator 900 described in FIG. 5A. The mass, and other components ofresonator 900 may be modeled as the RLC circuit of MEMS 952. MEMS 952includes resistor R 932 connected in series with inductor L 930 andcapacitor C 934. A first terminal of resistor R 932 connects to AC drivevoltage Vd 904. A second terminal of resistor R 932 connects to a firstterminal of inductor L 930. A second terminal of inductor L 930 connectsto a first terminal of capacitor C 934. A second terminal of capacitor C934 connects to a node 942, which also includes a connection tofeedthrough capacitance Cf 908, resistor R 935 and capacitor Cblock 940.The other terminal of Cblock 940 connects to a terminal, which mayoutput a sense signal to an amplifier. Bias voltage Vb 902 connects tothe same node 942 through resistor R 935.

Motional current, or sense current, i_(m) 958, caused by AC drivevoltage 904 moves through MEMS 952. The electrode and electricalconductor geometry may cause unwanted feedthrough current i_(f) 956. Thefeedthrough current i_(f) 956 adds to the motional current i_(m) 958caused by motion of the mechanical resonator at node 942 and is outputas i_(m)+i_(f) 954 to an amplifier. This total output current may readby the front-end electronics. The total current may cause the resonatortransfer function to be degraded, which may cause increasedaccelerometer noise. The additional feedthrough current may degradestability of the accelerometer bias if the resonator is driven far awayfrom mechanical resonance.

FIGS. 6A and 6B are schematic diagrams illustrating an example MEMS VBAconfigured with two sense electrodes. FIG. 6A shows a mechanical modelof an example single sense electrode VBA and FIG. 6B shows theequivalent electrical circuit. The arrangement of resonator 1000, andcircuit 1050, may cancel at least some of the unwanted feedthroughcurrent and reduce the effects of feedthrough capacitance.

In the example of FIG. 6A, mass 1010 connects to attachment point 1022through a spring 1016 with spring constant K and connects to attachmentpoint 1023 through variable drive capacitance Cd 1012. For the senseelectrodes, mass 1010 connects to attachment point 1024 through variablesense capacitance Cs− 1015 and to attachment point 1025 through variablesense capacitance Cs+ 1014.

AC drive voltage Vd 1004 connects to a drive electrode at attachmentpoint 1023 to excite mechanical motion in the resonator and cause mass1010 to move along the X-axis 1018. As described above in relation toFIG. 4, electrodes position and signal routing may create some parasiticcapacitance between the drive electrodes and sense electrodes. In theexample of resonator 1000, positive feedthrough capacitance Cf+ 1008 maybe caused by parasitic capacitance between the drive circuitry and thesense circuitry that includes Cs+ 1014. Negative feedthrough capacitanceCf− 1018 may be caused by parasitic capacitance between the drivecircuitry and the sense circuitry that includes Cs− 1015.

As described above in relation to FIG. 4, positive sense electrodes fora resonator, represented by Cs+ 1014, may produce positive current whenresonator tines move apart. Negative sense electrodes, represented byCs− 1015, may produce positive current when resonator tines movetogether. Thus, the sense electrodes are oriented to have dC/dx's ofsimilar magnitude but opposite sign. Routing of electrical signals 850,852 and 854 on the MEMS die may be configured to have similarfeedthrough capacitance between the drive and both positive and negativesense electrodes such that Cf+ 1008 and Cf− 1018 are approximatelyequal. Approximately equal in this disclosure means equal withinmanufacturing and measurement tolerances. Small variations duringmanufacturing in materials, process, and so on may cause smalldifferences such that, for example, Cf− 1018 and Cf+ 1008 may beapproximately equal rather than exactly equal. The sense outputs fromresonator 1000 may be processed by a differential amplifier 1020 so thatthe positive and negative feedthrough currents may approximately canceleach other.

In the example of FIG. 6B, circuit 1050 is an equivalent circuit ofresonator 1000 described in FIG. 6A. The mass, and other components ofresonator 900 may be modeled as two RLC circuits of MEMS 1052. For thepositive sense branch, MEMS 1052 includes resistor R 1032 connected inseries with inductor L 1030 and capacitor C 1034. A first terminal ofresistor R 1032 connects to AC drive voltage +Vd 1040. A second terminalof resistor R 1032 connects to a first terminal of inductor L 1030. Asecond terminal of inductor L 1030 connects to a first terminal ofcapacitor C 1034. A second terminal of capacitor C 1034 connects tooutput node 1042, which also includes a connection to feedthroughcapacitance Cf+ 1008. AC drive voltage +Vd 1040 and AC drive voltage −Vd1041 indicate that the drive voltages are opposite in phase. Thoughdepicted as two separate AC sources in the example of circuit 1050, inother examples, a single AC source may provide the drive signal andanalog circuitry, for example, may output AC drive signals of oppositephase. For example, resonator drive circuits 103A, 103B, 104A and 104Bdescribed above in relation to FIGS. 3A and 3B, may include AC drivecircuitry configured to provide drive signals to the resonators that areof opposite phase.

For the negative sense branch, MEMS 1052 includes resistor R 1033connected in series with inductor L 1031 and capacitor C 1035. A firstterminal of resistor R 1033 connects to AC drive voltage −Vd 1041. Asecond terminal of resistor R 1033 connects to a first terminal ofinductor L 1031. A second terminal of inductor L 1031 connects to afirst terminal of capacitor C 1035. A second terminal of capacitor C1035 connects to output node 1043, which also includes a connection tofeedthrough capacitance Cf− 1018.

Motional current caused by AC drive voltages 1040 and 1041 moves throughboth the positive branch of MEMS 1052, which includes R 1032, e.g.i_(m+) 1058, and through the negative branch, which includes R 1033,e.g. i_(m−) 1059. The electrode and electrical conductor geometry maycause unwanted feedthrough currents i_(f+) 1056 and i_(f−) 1057. On thepositive side, feedthrough current i_(f+) 1056 adds to the motionalcurrent i_(m+) 1058 caused by motion of the mechanical resonator and isoutput as i_(m+)+i_(f+) 1054 to one input of a differential amplifier1020. On the negative side, feedthrough current i_(f−) 1057 adds to themotional current i_(m−) 1059 and is output as i_(m−)+i_(f+) 1055 to asecond input of the differential amplifier 1020. In equation form, theresult may be described as:

-   -   positive and negative sense currents are approximately equal:        i_(m+)=−i_(m−)    -   positive and negative feedthrough capacitance are approximately        equal: C_(f+)=C_(f−) and i_(f+)=i_(f−)    -   therefore, the output of the differential amplifier is:        i_(diff)=i_(m+)+i_(f+)−(i_(f−)+i_(m−))=2*i_(m+)

FIG. 7A is a conceptual diagram illustrating a first resonator 1120 withadded masses, in accordance with one or more techniques of thisdisclosure. First resonator 1120 may be an example of resonators 18 ofFIG. 1 and first resonator 120 of FIG. 3B. First resonator 1120 mayinclude anchored combs 1122A-1122C (collectively, “anchored combs1122”), first mechanical beam 1124A, and second mechanical beam 1124(collectively, “mechanical beams 1124”). First mechanical beam 1124A mayinclude added masses 1162A-1162D (collectively, “added masses 1162”).Second mechanical beam 1124B may include added masses 1164A-1164D(collectively, “added masses 1164”).

In some examples, anchored comb 1122A includes one or more anchored combsections, anchored comb 1122B includes one or more anchored combsections, and anchored comb 1122C includes one or more anchored combsections. In some examples, any one or combination of the anchored combsections of anchored comb 1122A may include one or more electrodes of afirst set of electrodes (e.g., first set of electrodes 128A of FIG. 3B).In some examples, any one or combination of the anchored comb sectionsof anchored comb 1122B may include one or more electrodes of a secondset of electrodes (e.g., second set of electrodes 128A). In someexamples, any one or combination of the anchored comb sections ofanchored comb 1122C may include one or more electrodes of a third set ofelectrodes (e.g., third set of electrodes 128C).

In some examples, a resonator driver circuit may deliver a drive signalto first resonator 1120 via any one or combination of the first set ofelectrodes, the second set of electrodes, and the third set ofelectrodes, causing first resonator 1120 to vibrate at a resonantfrequency. For example, the first mechanical beam 1124A and the secondmechanical beam 1124B may vibrate at the resonant frequency. In turn,the first set of electrodes may generate a first electrical signal, thesecond set of electrodes may generate a second electrical signal, andthe third set of electrodes may generate a third electrical signal.First resonator 1120 may output the first electrical signal, the secondelectrical signal, and the third electrical signal to processingcircuitry (not illustrated in FIG. 4A) which is configured to determinethe resonant frequency of the first resonator 1120 based on the firstelectrical signal, the second electrical signal, and the thirdelectrical signal.

In some examples, the resonant frequency of first resonator 1120 may becorrelated with an amount of force applied to first resonator 1120 by aproof mass, such as proof mass 32 of FIG. 1 and proof mass 112 of FIG.3B. For example, a first end 1182 of first resonator 1120 may be fixedto a resonator connection structure (e.g., resonator connectionstructure 16 of FIG. 1 and resonator connection structure 116 of FIG.3B) and a second end 1184 of first resonator 1120 may be fixed to theproof mass. If the proof mass rotates towards first resonator 1120 inresponse to an acceleration in a first direction, the proof mass mayapply a compression force to first resonator 1120. If the proof massrotates away from first resonator 1120 in response to an acceleration ina second direction, the proof mass may apply a tension force to firstresonator 1120. In some examples, i_(f) acceleration is at zero m/s²,the proof mass may apply no force to first resonator 1120. The resonantfrequency of first resonator 1120 may decrease as the compression forceapplied by the proof mass increases in response to an increase inacceleration in the first direction, and the resonant frequency of firstresonator 1120 may increase as the tension force applied by the proofmass increases in response to an increase in acceleration in the seconddirection. In this way, a relationship may exist between the resonantfrequency of first resonator 1120 and the acceleration of anaccelerometer which includes first resonator 1120.

Added masses 1162 and added masses 1164 may affect the relationshipbetween acceleration and the resonant frequency of first resonator 1120.For example, a quadratic nonlinearity coefficient defining therelationship between the acceleration and the resonant frequency offirst resonator 1120 may be smaller as compared with a quadraticnonlinearity coefficient defining a relationship between an accelerationand a resonant frequency of a resonator which does not include addedmasses 1162 and added masses 1164. It may be beneficial for therelationship between acceleration and the resonant frequency of firstresonator 1120 to be as close to linear as possible (e.g., the quadraticnonlinearity coefficient being as small as possible) in order to ensurethat the electrical signals generated by first resonator 1120 allowprocessing circuitry to accurately determine acceleration.

In some examples, added mass 1162A and added mass 1162B may be placed ata location along first mechanical beam 1124A that is within a range from25% to 45% along a length of first mechanical beam 1124A from first end1156 to second end 1157. For example, added mass 1162A and added mass1162B may be placed at a location that is 35% of a distance betweenfirst end 1156 to second end 1157. In some examples, added mass 1162Cand added mass 1162D may be placed at a location along first mechanicalbeam 1124A that is within a range from 55% to 75% along a length offirst mechanical beam 1124A from first end 1156 to second end 1157. Forexample, added mass 1162C and added mass 1162D may be placed at alocation that is 65% of a distance between first end 1156 to second end1157.

In some examples, added mass 1164A and added mass 1164B may be placed ata location along second mechanical beam 1124B that is within a rangefrom 25% to 45% along a length of second mechanical beam 1124B fromfirst end 1158 to second end 1159. For example, added mass 1164A andadded mass 1164B may be placed at a location that is 35% of a distancebetween first end 1158 to second end 1159. In some examples, added mass1164C and added mass 1164D may be placed at a location along secondmechanical beam 1124B that is within a range from 55% to 75% along alength of second mechanical beam 1124B from first end 1158 to second end1159. For example, added mass 1164C and added mass 1164D may be placedat a location that is 65% of a distance between first end 1158 to secondend 1159.

FIG. 4B is a conceptual diagram illustrating a portion of firstresonator 1120 of FIG. 4A including added masses 1162A and 1162B, inaccordance with one or more techniques of this disclosure. For example,first mechanical beam 1124A includes a primary member 1190 and a set ofsecondary members 1192A-1192D (collectively, “set of secondary members1192”). As seen in FIG. 4B, each secondary member of the set ofsecondary members 1192 extends normal to primary member 1190. Firstmechanical beam 1124A may include additional secondary members andadditional other components that are not illustrated in FIG. 4B. Eachsecondary member of the set of secondary members 1192 may besubstantially the same, except that secondary member 1192C includesadded mass 1162A and added mass 1162B.

FIG. 8A is a conceptual diagram illustrating a second resonator 1230forming gaps, in accordance with one or more techniques of thisdisclosure. Second resonator 1230 may be an example of second resonator130 of FIG. 3B. Second resonator 1230 may include anchored combs1232A-1232C (collectively, “anchored combs 1232”), third mechanical beam1234A, and fourth mechanical beam 1234B (collectively, “mechanical beams1234”). Third mechanical beam 1234A may form gaps 1262A-1262D(collectively, “gaps 1262”). Fourth mechanical beam 1234B may form gaps1264A-1264D (collectively, “gaps 1264”).

In some examples, anchored comb 1232A may include one or more anchoredcomb sections, anchored comb 1232B may include one or more anchored combsections, and anchored comb may include one or more anchored combsections. In some examples, any one or combination of the anchored combsections of anchored comb 1232A may include one or more electrodes of afourth set of electrodes (e.g., fourth set of electrodes 138A of FIG.3B). In some examples, any one or combination of the anchored combsections of anchored comb 1232B may include one or more electrodes of afifth set of electrodes (e.g., fifth set of electrodes 138B). In someexamples, any one or combination of the anchored comb sections ofanchored comb 1232C may include one or more electrodes of a sixth set ofelectrodes (e.g., sixth set of electrodes 138C).

In some examples, a resonator driver circuit may deliver a drive signalto second resonator 1230 via any one or combination of the fourth set ofelectrodes, the fifth set of electrodes, and the sixth set ofelectrodes, causing second resonator 1230 to vibrate at a resonantfrequency. For example, the third mechanical beam 1234A and the fourthmechanical beam 1234B may vibrate at the resonant frequency of secondresonator 1230. In turn, the fourth set of electrodes may generate afourth electrical signal, the fifth set of electrodes may generate afifth electrical signal, and the sixth set of electrodes may generate asixth electrical signal. Second resonator 1230 may output the fourthelectrical signal, the fifth electrical signal, and the sixth electricalsignal to processing circuitry (not illustrated in FIG. 8A) which isconfigured to determine the resonant frequency of the second resonator1230 based on the fourth electrical signal, the fifth electrical signal,and the sixth electrical signal.

In some examples, the resonant frequency of second resonator 1230 may becorrelated with an amount of force applied to second resonator 1230 by aproof mass, such as proof mass 112 of FIG. 3B. For example, a first end1282 of second resonator 1230 may be fixed to the proof mass and asecond end 1284 of second resonator 1230 may be fixed to a resonatorconnection structure (e.g., resonator connection structure 116 of FIG.3B). If the proof mass rotates away from second resonator 1230 inresponse to an acceleration in a first direction, the proof mass mayapply a tension force to second resonator 1230. If the proof massrotates towards second resonator 1230 in response to an acceleration ina second direction, the proof mass may apply a compression force tosecond resonator 1230. In some examples, if acceleration is at zerom/s², the proof mass may apply no force to second resonator 1230. Theresonant frequency of second resonator 1230 may decrease as thecompression force applied by the proof mass increases in response to anincrease in acceleration in the second direction, and the resonantfrequency of second resonator 1230 may increase as the tension forceapplied by the proof mass increases in response to an increase inacceleration in the first direction. In this way, a relationship mayexist between the resonant frequency of second resonator 1230 and theacceleration of an accelerometer which includes second resonator 1230.

Gaps 1262 and gaps 1264 may affect the relationship between accelerationand the resonant frequency of second resonator 1230. For example, aquadratic nonlinearity coefficient defining the relationship between theacceleration and the resonant frequency of second resonator 1230 may besmaller as compared with a quadratic nonlinearity coefficient defining arelationship between an acceleration and a resonant frequency of aresonator which does not include gaps 1262 and gaps 1264. It may bebeneficial for the relationship between acceleration and the resonantfrequency of second resonator 1230 to be as close to linear as possible(e.g., the quadratic nonlinearity coefficient being as small aspossible) in order to ensure that the electrical signals generated bysecond resonator 1230 allow processing circuitry to accurately determineacceleration. In some examples, gaps 1262 represent “holes” where addedmasses 1162 are included on first resonator 1120 of FIGS. 7A-7B. In someexamples, gaps 1264 represent holes where added masses 1164 are includedon first resonator 1120 of FIGS. 7A-7B. The gaps or holes for the addedmasses on the resonators are different than the holes in the proof massconfigured to tune mechanical modes, as described above in relation toFIG. 4.

In some examples, gap 1262A and gap 1262B may be placed at a locationalong third mechanical beam 1234A that is within a range from 25% to 45%along a length of third mechanical beam 1234A from first end 1256 tosecond end 1257. For example, gap 1262A and gap 1262B may be placed at alocation that is 35% of a distance between first end 1256 to second end1257. In some examples, gap 1262C and gap 1262D may be placed at alocation along third mechanical beam 1234A that is within a range from55% to 75% along a length of third mechanical beam 1234A from first end1256 to second end 1257. For example, gap 1262C and gap 1262D may beplaced at a location that is 65% of a distance between first end 1256 tosecond end 1257.

In some examples, gap 1264A and gap 1264B may be placed at a locationalong fourth mechanical beam 1234B that is within a range from 25% to45% along a length of fourth mechanical beam 1234B from first end 1258to second end 1259. For example, gap 1264A and gap 1264B may be placedat a location that is 35% of a distance between first end 1258 to secondend 1259. In some examples, gap 1264C and gap 1264D may be placed at alocation along fourth mechanical beam 1234B that is within a range from55% to 75% along a length of fourth mechanical beam 1234B from first end1258 to second end 1259. For example, gap 1264C and gap 1264D may beplaced at a location that is 65% of a distance between first end 1258 tosecond end 1259.

FIG. 8B is a conceptual diagram illustrating a portion of secondresonator 1230 of FIG. 8A including gaps 1262A and 1262B, in accordancewith one or more techniques of this disclosure. For example, thirdmechanical beam 1234A includes a primary member 1290 and a set ofsecondary members 1292A-1292D (collectively, “set of secondary members1292”). As seen in FIG. 8B, each secondary member of the set ofsecondary members 1292 extends normal to primary member 1290. Thirdmechanical beam 1234A may include additional secondary members andadditional other components that are not illustrated in FIG. 8B. Eachsecondary member of the set of secondary members 1292 may besubstantially the same, except a distance between secondary member 1292Cand 1292D is greater than a distance between any other pair ofconsecutive secondary members of the set of secondary members 1292.

FIG. 9 is a graph illustrating a first plot 1310 representing aquadratic nonlinearity coefficient as a function of added mass positionand a second plot 1320 representing a zero acceleration resonantfrequency difference as a function of added mass position, in accordancewith one or more techniques of this disclosure. For example, the“Location of Added Mass” may represent a position of added masses suchas added mass 1162A and added mass 1162B on first mechanical beam 1124A,depicted in FIG. 7A, where the position is a percentage of a length offirst mechanical beam 1124A extending from first end 1156 to second end1157. As seen in first plot 610 of FIG. 6, the quadratic nonlinearitycoefficient (K₂) is zero when the position of added mass 1162A and addedmass 1162B is 35% of the length of first mechanical beam 1124A.Additionally, as seen at point 1330 of second plot 1320, a differencebetween the resonant frequency of first resonator 1120 and a differencebetween the resonant frequency of second resonator 1230 may is nonzerowhen the position of added mass 1162A and added mass 1162B is 35% of thelength of first mechanical beam 1124A. As such, it may be beneficial forthe position of added mass 1162A and added mass 1162B to be 35% of thelength of first mechanical beam 1124A, since the quadratic nonlinearitycoefficient is zero and the frequency difference is nonzero. μ

In some examples, point 1330 may represent an ideal location of addedmass 1162A and added mass 1162B along first mechanical beam 1124A. Insome examples, a resonant frequency of first resonator 1120 at zeroacceleration may be within a range from 25 kilohertz (KHz) to 30 KHz. Insome examples, a resonant frequency of second resonator 1230 at zeroacceleration may be within a range from 25 kilohertz (KHz) to 30 KHz. Insome examples, a difference between the resonant frequency of firstresonator 1120 at zero acceleration and a resonant frequency of secondresonator 1230 at zero acceleration may be within a range from 250 Hertz(Hz) to 3500 Hz when added mass 1162A and added mass 1162B is placed at35% of a length of first mechanical beam 1124A.

FIG. 10 is a flow diagram illustrating an example operation fordetermining an acceleration of a VBA, in accordance with one or moretechniques of this disclosure. FIG. 7 is described with respect toprocessing circuitry 102, resonator driver circuits 104, and proof massassembly 111 of FIG. 3B. However, the techniques of FIG. 7 may beperformed by different components of system 101, system 100 of FIG. 3A,or by additional or alternative accelerometer systems.

Resonator driver circuit 104A may deliver a set of drive signals tofirst resonator 120 (1402). Resonator driver circuit 104A may beelectrically coupled to first resonator 120. Resonator driver circuit104A may output the set of drive signals to first resonator 120, causingfirst resonator 120 to vibrate at a resonant frequency. Processingcircuitry 102 may receive, via resonator driver circuit 104A, one ormore electrical signals indicative of a frequency of first mechanicalbeam 124A and second mechanical beam 124B (1404). Subsequently,processing circuitry 102 may determine, based on the one or moreelectrical signals, the frequency of first mechanical beam 124A andsecond mechanical beam 124B (1406). The mechanical vibration frequencyof first mechanical beam 124A and the mechanical vibration frequency ofsecond mechanical beam 124B may represent a resonant frequency of firstresonator 120. The resonant frequency of first resonator 120 may becorrelated with an acceleration of a VBA, such as VBA 110 of FIG. 2. Assuch, processing circuitry 102 may calculate, based on the frequency offirst mechanical beam 124A and the frequency of second mechanical beam124B, the acceleration of VBA 110 (1408).

Although the example operation is described with respect to firstresonator 120, processing circuitry 102 may additionally oralternatively determine a resonant frequency of second resonator 130. Insome examples, processing circuitry 102 may be configured to determine adifference between the resonant frequency of first resonator 120 and theresonant frequency of second resonator 130 and calculate theacceleration based on a difference in the resonant frequencies.

In one or more examples, the accelerometers described herein may utilizehardware, software, firmware, or any combination thereof for achievingthe functions described. Those functions implemented in software may bestored on or transmitted over, as one or more instructions or code, acomputer-readable medium and executed by a hardware-based processingunit. Computer-readable media may include computer-readable storagemedia, which corresponds to a tangible medium such as data storagemedia, or communication media including any medium that facilitatestransfer of a computer program from one place to another, e.g.,according to a communication protocol. In this manner, computer-readablemedia generally may correspond to (1) tangible computer-readable storagemedia which is non-transitory or (2) a communication medium such as asignal or carrier wave. Data storage media may be any available mediathat can be accessed by one or more computers or one or more processorsto retrieve instructions, code and/or data structures for implementationof the techniques described in this disclosure.

Instructions may be executed by one or more processors within theaccelerometer or communicatively coupled to the accelerometer. The oneor more processors may, for example, include one or more DSPs, generalpurpose microprocessors, application specific integrated circuits ASICs,FPGAs, or other equivalent integrated or discrete logic circuitry.Accordingly, the term “processor,” as used herein may refer to any ofthe foregoing structure or any other structure suitable forimplementation of the techniques described herein. In addition, in someaspects, the functionality described herein may be provided withindedicated hardware and/or software modules configured for performing thetechniques described herein. Also, the techniques could be fullyimplemented in one or more circuits or logic elements.

The techniques of this disclosure may be implemented in a wide varietyof devices or apparatuses that include integrated circuits (ICs) or setsof ICs (e.g., chip sets). Various components, modules, or units aredescribed in this disclosure to emphasize functional aspects of devicesconfigured to perform the disclosed techniques, but do not necessarilyrequire realization by different hardware units. Rather, various unitsmay be combined or provided by a collection of interoperative hardwareunits, including one or more processors as described above, inconjunction with suitable software and/or firmware.

Various examples of the disclosure have been described. These and otherexamples are within the scope of the following claims.

1. A vibrating beam accelerometer (VBA) device, the device comprising: aresonator comprising: a resonator beam; a drive electrode; and a firstsense electrode and a second sense electrode, wherein: the first senseelectrode is located on a first side of the resonator beam, the secondsense electrode is located on a second side of the resonator beamopposite the first side such that a first change in capacitance withrespect to displacement (dC₁/dx) for the first sense electrode isapproximately equal in magnitude to a second change in capacitance withrespect to displacement (dC₂/dx) for the second sense electrode andopposite in sign; and electrical signal routing: comprising: a drivesignal path coupled to the drive electrode; a first sense signal pathcoupled to the first sense electrode; and a second sense signal pathcoupled to the second sense electrode, wherein the electrical signalrouting is configured to produce: a first parasitic capacitance betweenthe drive signal path and the first sense signal path that generates afirst parasitic feedthrough current; and a second parasitic capacitancebetween the drive signal path and the second sense signal path, thatgenerates a second parasitic feedthrough current, such that the firstparasitic feedthrough current and the second parasitic feedthroughcurrent are approximately equal in magnitude.
 2. The device of claim 1,wherein the drive electrode is a first drive electrode on the first sideof the resonator beam, the device further comprising a second driveelectrode located on the second side of the resonator beam, wherein thefirst drive electrode is configured to receive a first drive signal,wherein the second drive electrode is configured to receive a seconddrive signal, and wherein the first drive signal is opposite in phase tothe second drive signal.
 3. The device of claim 2, wherein the firstdrive signal and the second drive signal are alternating current (AC)drive signals.
 4. The device of claim 1, wherein the first senseelectrode is coupled to a first anchored comb on the first side of theresonator beam, and wherein the second sense electrode is coupled to asecond anchored comb on the second side of the resonator beam.
 5. Thedevice of claim 4, wherein the first sense electrode produces a positivecurrent when the first anchored comb moves apart from the resonatorbeam, and wherein the second sense electrode produces a produce positivecurrent when the second anchored comb moves closer to the resonatorbeam.
 6. The device of claim 1 further comprising: a proof mass, whereinthe proof mass is a pendulous proof mass; a support base defining afirst plane; a resonator connection structure mechanically connected tothe support base with an anchor, wherein the resonator connectionstructure is in a second plane parallel to the first plane; a hingeflexure configured to connect the pendulous proof mass to the resonatorconnection structure, wherein the hinge flexure suspends the pendulousproof mass parallel to the support base at the anchor, and wherein thependulous proof mass rotates about the hinge flexure in the second planein response to an acceleration of the device parallel to the first planeof the support base, wherein: the resonator is configured to connect thependulous proof mass to the resonator connection structure and to flexin the second plane based on a rotation of the pendulous proof massabout the hinge flexure, the pendulous proof mass, the hinge flexure,and the one or more resonators are in the second plane.
 7. The device ofclaim 6, further comprising a support flexure coupled to the pendulousproof mass, wherein the support flexure is configured to restrictout-of-plane motion of the pendulous proof mass with respect to thesecond plane.
 8. The device of claim 6, wherein the resonator beam isconfigured to flex in a direction substantially perpendicular to a longaxis of the resonator connection structure.
 9. The device of claim 1,wherein the resonator is a first resonator, the device furthercomprising at least a second resonator, wherein each of the firstresonator and the second resonator resonate at a respective drivenresonant frequency.
 10. A method comprising: receiving, by processingcircuitry, one or more electrical signals indicative of a frequency of afirst resonator beam and a frequency of a second resonator beam from avibrating beam accelerometer (VBA), wherein the VBA comprises: aresonator comprising: the first resonator beam; a drive electrode; and afirst sense electrode and a second sense electrode, wherein: the firstsense electrode is located on a first side of the resonator beam, thesecond sense electrode is located on a second side of the resonator beamopposite the first side such that a first change in capacitance withrespect to displacement (dC₁/dx) for the first sense electrode isapproximately equal in magnitude to a second change in capacitance withrespect to displacement (dC₂/dx) for the second sense electrode andopposite in sign; and electrical signal routing: comprising: a drivesignal path coupled to the drive electrode; a first sense signal pathcoupled to the first sense electrode; and a second sense signal pathcoupled to the second sense electrode, wherein the electrical signalrouting is configured to produce: a first parasitic capacitance betweenthe drive signal path and the first sense signal path that generates afirst parasitic feedthrough current; and a second parasitic capacitancebetween the drive signal path and the second sense signal path, thatgenerates a second parasitic feedthrough current, such that the firstparasitic feedthrough current and the second parasitic feedthroughcurrent are approximately equal in magnitude; determining, by theprocessing circuitry and based on the one or more electrical signals,the frequency of the first resonator beam and the frequency of thesecond resonator beam; and calculating, by the processing circuitry andbased on the frequency of the first resonator beam and the frequency ofthe second resonator beam, an acceleration of the VBA.
 11. The method ofclaim 10, wherein the drive electrode is a first drive electrode on thefirst side of the resonator beam, the device further comprising a seconddrive electrode located on the second side of the resonator beam,wherein the first drive electrode is configured to receive a first drivesignal, wherein the second drive electrode is configured to receive asecond drive signal, and wherein the first drive signal is opposite inphase to the second drive signal.
 12. The method of claim 10, whereinthe resonator is a first resonator, the VBA further comprising a secondresonator, the method further comprises calculating, based on thedifference between the frequency of the first resonator and thefrequency of the second resonator, the acceleration of the proof massassembly.
 13. A system for determining acceleration, the systemcomprising: processing circuitry coupled to a resonator driver circuitand configured to cause the resonator driver circuit to output aresonator driver signal; a vibrating beam accelerometer (VBA) devicecomprising a resonator configured to receive the resonator driversignal, the resonator comprising: a resonator beam; a drive electrode;and a first sense electrode and a second sense electrode, wherein: thefirst sense electrode is located on a first side of the resonator beam,the second sense electrode is located on a second side of the resonatorbeam opposite the first side such that a first change in capacitancewith respect to displacement (dC₁/dx) for the first sense electrode isapproximately equal in magnitude to a second change in capacitance withrespect to displacement (dC₂/dx) for the second sense electrode andopposite in sign; and electrical signal routing: comprising: a drivesignal path coupled to the drive electrode; a first sense signal pathcoupled to the first sense electrode; and a second sense signal pathcoupled to the second sense electrode, wherein the electrical signalrouting is configured to produce: a first parasitic capacitance betweenthe drive signal path and the first sense signal path that generates afirst parasitic feedthrough current; and a second parasitic capacitancebetween the drive signal path and the second sense signal path, thatgenerates a second parasitic feedthrough current, such that the firstparasitic feedthrough current and the second parasitic feedthroughcurrent are approximately equal in magnitude.
 14. The system of claim13, wherein the drive electrode is a first drive electrode on the firstside of the resonator beam, the device further comprising a second driveelectrode located on the second side of the resonator beam, wherein thefirst drive electrode is configured to receive a first drive signal,wherein the second drive electrode is configured to receive a seconddrive signal, and wherein the first drive signal is opposite in phase tothe second drive signal.
 15. The system of claim 14, wherein the firstdrive signal and the second drive signal are alternating current (AC)drive signals.
 16. The system of claim 13, wherein the first senseelectrode is coupled to a first anchored comb on the first side of theresonator beam, and wherein the second sense electrode is coupled to asecond anchored comb on the second side of the resonator beam.
 17. Thesystem of claim 16, wherein the first sense electrode produces apositive current when the first anchored comb moves apart from theresonator beam, and wherein the second sense electrode produces aproduce positive current when the second anchored comb moves closer tothe resonator beam.
 18. The system of claim 13, wherein the VBA furthercomprises: a proof mass, wherein the proof mass is a pendulous proofmass; a support base defining a first plane; a resonator connectionstructure mechanically connected to the support base with an anchor,wherein the resonator connection structure is in a second plane parallelto the first plane; a hinge flexure configured to connect the pendulousproof mass to the resonator connection structure, wherein the hingeflexure suspends the pendulous proof mass parallel to the support baseat the anchor, and wherein the pendulous proof mass rotates about thehinge flexure in the second plane in response to an acceleration of thedevice parallel to the first plane of the support base, wherein: theresonator is configured to connect the pendulous proof mass to theresonator connection structure and to flex in the second plane based ona rotation of the pendulous proof mass about the hinge flexure, thependulous proof mass, the hinge flexure, and the one or more resonatorsare in the second plane.
 19. The system of claim 13, further comprisinga support flexure coupled to the pendulous proof mass, wherein thesupport flexure is configured to restrict out-of-plane motion of thependulous proof mass with respect to the second plane.
 20. The system ofclaim 13, wherein the resonator is a first resonator, the VBA furthercomprising a second resonator, wherein each of the first resonator andthe second resonator resonate at a respective driven resonant frequency.